Fitting a Log-Periodic Bubble Model to KLSE Index Data

# forecasting crash time of KLSE index (1991-1994)


# forecasting crash time of KLSE index (1991-1994)












Price deviation = financial bubbles.

i try to fit the following stock price index to predict recession. I couldn't fit the model with the data(Data are not available in yahoo finance for the particular period, so I bought the data and typed). Can anyone help me to point out my mistakes??? the codes (R 2.14.2) are as follows:

```
 library(tseries)
 library(zoo)
 ts<- structure(c(505.47, 528.03, 526.19, 553.65, 543.49, 541.74, 541.01, 535.38, 545.80, 553.46, 559.10, 560.05, 561.83, 562.50, 557.92, 559.16, 552.60, 548.78, 549.41, 544.66, 541.34, 536.32, 529.30, 524.20, 520.57, 521.03,  523.08, 526.70, 530.70, 522.69, 521.81, 521.77, 518.20, 513.11, 508.25, 508.26, 508.22, 507.37, 510.36, 518.80, 514.59, 517.24, 517.59, 516.60, 514.99, 522.36, 525.98, 533.54, 530.44, 535.43, 534.69, 530.30, 531.40, 537.03, 531.09, 531.67, 533.16, 536.19, 554.57, 556.73, 555.85, 553.21, 545.74, 528.60, 535.64, 535.72, 537.59, 539.04, 537.38, 537.07, 536.18, 532.32, 532.09, 528.21, 528.38, 529.41, 529.32, 530.33, 531.42, 531.75, 530.90, 532.69, 537.85, 542.45, 543.30, 540.61, 541.13, 540.64, 545.52, 549.78,  550.48,  551.80, 554.38, 556.22, 552.16, 552.99, 557.34, 555.66, 553.48, 552.37, 551.90, 548.69, 546.63,  552.28,  569.23, 569.65, 572.23, 570.57, 572.27, 571.64, 568.78, 570.55, 569.84, 573.28, 568.75, 570.64, 575.81,  589.84, 603.35, 604.45, 600.76,  594.63, 595.75, 597.78,  607.67, 618.72, 619.06, 615.73,  610.86,  602.29,  603.16,  600.66, 605.06, 601.93, 597.83, 598.64,  593.93, 590.94, 584.01,  586.95, 588.36, 592.42,  595.22,  591.74, 594.49, 600.40, 597.96, 603.19, 609.33, 609.90, 607.40, 604.27, 602.71, 597.69, 593.21, 588.37, 588.12, 586.46, 573.61, 563.69, 571.31, 567.51, 564.51, 568.19, 575.83, 575.75, 572.46, 572.57, 573.95, 582.90, 583.71, 581.02, 583.62, 585.12, 591.63, 597.47, 603.02,  604.46,  603.56, 605.71, 603.97, 603.08,  598.65, 593.03, 590.34, 590.91, 594.09, 592.86, 592.48, 591.93, 592.52, 591.20, 600.17, 589.09, 585.33,  586.74, 588.43, 586.23, 587.16, 585.39, 584.67, 589.52, 590.55, 600.17, 602.15, 603.19, 596.50, 596.58,  594.05, 593.52, 594.00, 598.60, 596.55, 591.14, 592.33, 596.47, 596.08, 595.75, 596.70,  595.97,  603.72,  611.57, 616.08, 617.94, 612.36, 611.74,  605.33, 602.76,  605.16, 608.79, 602.24, 593.53,  589.70,  585.77,  590.71, 598.56,  601.53, 601.39, 603.54, 602.58, 598.27, 597.11, 595.16, 597.80, 594.57, 592.18,  581.94, 568.25, 556.24, 560.01, 564.21, 567.66, 565.56, 561.27, 559.51, 567.56, 574.73, 573.50, 572.92,  577.71, 581.17, 584.84, 586.61, 584.19, 580.79, 583.74, 585.91, 585.15, 587.13, 587.54, 587.99, 588.32, 590.84,  593.07, 602.60, 610.65, 605.93, 602.28, 598.10, 594.59, 594.33, 590.70, 592.04, 593.08, 592.63, 602.72,  605.13, 606.56, 606.17, 608.05, 612.33, 614.96, 615.85, 623.87, 630.07, 633.32, 633.31, 637.13, 641.31,  649.06, 653.07, 659.33, 660.35, 654.60, 648.93, 645.32, 646.80, 652.23, 650.62,  646.25, 641.90, 641.77,  637.39, 642.60, 643.79, 643.02, 641.84, 638.79, 640.48, 641.89, 637.23, 641.51, 636.40,  637.61, 635.56,  635.93, 633.52, 633.94, 635.26,  632.54, 628.88, 632.89, 636.11, 641.08, 643.60, 644.94, 645.04, 646.39,  645.03, 642.95, 642.66, 643.96, 632.83, 630.89, 633.66, 636.26, 629.51, 621.46, 616.46, 614.28,  619.81,  617.49, 624.37, 624.12, 622.61, 625.93, 626.34, 624.89, 618.41, 624.49, 628.38, 639.24, 642.95, 644.90,  641.60, 639.97, 638.62, 635.84, 635.42, 634.91, 635.01, 625.81, 623.11, 629.43, 635.59, 632.28, 634.22,  638.83, 638.19, 634.87, 637.00, 636.44, 636.67, 638.34, 637.93, 631.79, 637.37, 637.25, 638.05, 634.81, 637.79, 640.39, 640.24, 636.33, 634.65, 634.42, 638.87, 638.92, 643.25, 649.56, 651.45, 656.13,  655.89,  661.35, 657.23, 655.24, 657.13, 655.58, 660.60, 660.73, 662.02, 664.95, 672.53, 691.70, 691.45, 691.65, 693.44, 692.57, 695.43, 705.00, 719.61, 717.37, 706.08, 706.46, 712.95, 716.54, 710.99, 712.67,  718.04,  720.00, 720.36, 725.46, 729.43,  735.11, 729.35, 724.48, 731.37, 735.39, 736.07, 735.25, 740.06,  741.27,  735.06, 732.15,  728.16, 736.28, 734.93, 737.53, 746.29, 743.16, 739.42, 736.51, 720.46, 735.25,  724.96, 717.96, 701.66, 708.80, 722.07, 720.58, 721.17, 719.84, 734.73, 732.51, 731.67, 732.66,  733.98, 728.05, 722.82, 718.86, 719.30, 714.23, 735.78, 742.50, 745.90, 761.60, 759.76, 757.65, 758.86, 755.57, 763.97,  764.70, 766.08, 763.46, 771.67, 781.99, 785.49, 778.66, 779.87, 780.60, 780.42, 776.16, 771.91, 772.76,  784.91, 791.02, 798.82, 805.51, 805.26, 805.47, 805.72, 811.78, 808.49, 821.00, 851.10, 851.40, 848.40, 849.70, 842.50, 833.00, 820.70, 820.30, 817.70, 816.40, 819.70, 819.60, 816.40, 818.60, 819.30,  830.30,  837.80, 846.10, 849.90, 846.50, 853.83, 859.87, 852.26, 859.87, 865.77, 874.34, 884.62, 895.15, 905.71,  911.38, 919.03, 927.46, 914.53, 926.16, 922.95, 937.09, 934.11, 930.49, 929.85, 934.53, 946.72, 971.99,  967.05, 972.36, 982.03, 977.06, 944.94, 921.52, 937.66, 950.89, 967.60, 972.47, 961.37, 951.30,  957.81,  956.57, 984.92, 989.40, 966.88, 970.30,  970.31,  976.34, 972.10, 996.45, 1015.42, 1017.51, 1023.92, 1041.11,  1063.25, 1060.79, 1067.34, 1075.85, 1090.35, 1092.66, 1116.09, 1112.59, 1109.53, 1098.08, 1096.61, 1121.38, 1152.24, 1178.46, 1205.28, 1223.05, 1231.86, 1231.73, 1275.32, 1288.85, 1313.35, 1314.46, 1248.69), .Dim = c(595L, 1L), .Dimnames = list(NULL, "Close"), index = structure(c(7900,7901, 7902, 7903, 7904, 7907, 7908, 7909, 7910, 7911, 7914, 7915, 7916, 7917, 7918, 7921, 7922,  7923,7924, 7925, 7928, 7929, 7930, 7931, 7935, 7936, 7937, 7938,7939, 7942, 7943, 7944, 7945,7946,  7949, 7950, 7951, 7952, 7953, 7956, 7957, 7958, 7959, 7960, 7963, 7964, 7965,  7966, 7967, 7970,  7971,   7972, 7973, 7974,  7977, 7979, 7980, 7981, 7984, 7985,7986, 7987, 7988, 7991, 7992, 7993, 7994, 7995,  7998, 7999, 8000, 8001, 8002, 8005, 8006, 8007,8008,  8009, 8012, 8013, 8014, 8015, 8016, 8019, 8020,   8021, 8022,  8023, 8026, 8027, 8029, 8030, 8033, 8034, 8036,8037, 8040, 8041,  8042, 8043, 8044, 8047,  8048, 8049, 8050, 8051, 8054, 8055, 8056, 8057, 8058, 8061, 8062, 8063, 8064, 8065, 8071, 8072, 8075,  8076, 8077, 8078, 8079, 8082, 8083, 8084, 8085, 8086, 8089, 8090, 8091,8092, 8093,8096, 8097, 8098,  8099,8100,8103, 8104, 8105, 8106, 8107, 8110, 8111, 8112, 8113, 8114, 8117, 8118, 8119, 8120,  8121,  8124, 8125, 8126, 8127, 8128, 8133, 8134, 8135,8138, 8139, 8140, 8141, 8142,8145,8146, 8147, 8148,  8149, 8152, 8153,8154, 8155, 8159, 8160,8161, 8162, 8163, 8166, 8167, 8168, 8169, 8170, 8174, 8175,  8176, 8177, 8180, 8181, 8182,  8183, 8184, 8187, 8188, 8189, 8190, 8191, 8194, 8195, 8196, 8198,  8201,  8202, 8203, 8204, 8205, 8208, 8209, 8210, 8211, 8212, 8215, 8216, 8217, 8219, 8222, 8223, 8224,  8225,  8226, 8229, 8230, 8231, 8232, 8233, 8236, 8237, 8238, 8239, 8240, 8243, 8244, 8245, 8246, 8247,  8250, 8251, 8252, 8253, 8254, 8257, 8258,8259, 8260, 8261, 8264, 8265, 8266, 8267, 8268, 8271, 8272,  8273,  8274, 8275, 8279, 8280, 8281, 8282, 8285, 8286,  8288, 8289, 8292, 8293, 8294, 8295, 8296, 8299,  8300,  8301, 8302, 8303, 8306, 8307, 8308, 8309, 8310,8313, 8314, 8315, 8316, 8317, 8320, 8321, 8322,  8323,  8324, 8327, 8328, 8329, 8330, 8331, 8335, 8336, 8337, 8338, 8341, 8342, 8343, 8344, 8345, 8348, 8349,  8350, 8351, 8352, 8355, 8356, 8357, 8358, 8359, 8362, 8363, 8364, 8365, 8366, 8369, 8370, 8371, 8372,  8373, 8376, 8377, 8378, 8379,8380,8383, 8384, 8385, 8386, 8387, 8390,8391,8392, 8393,8397,8398,  8399, 8400, 8404, 8405, 8406,8407,  8408,8411, 8412, 8413, 8414, 8415, 8418, 8419,8420, 8421, 8426,  8427, 8428, 8429, 8433, 8434, 8435, 8436,8439, 8440, 8441, 8442, 8443, 8446, 8447, 8448, 8449, 8450,  8453,  8454, 8455, 8456, 8457, 8460, 8461, 8462,  8463, 8464, 8467, 8468, 8469, 8470, 8471, 8474,  8475, 8476, 8477, 8478, 8481, 8482, 8488, 8489, 8490, 8491,  8492, 8495, 8496,  8497, 8498, 8499, 8502, 8503, 8504, 8505, 8506, 8509, 8510, 8511, 8512, 8513, 8516, 8517, 8518, 8519, 8520, 8523, 8524, 8525, 8527, 8530,  8531, 8532, 8533, 8534, 8537, 8538,  8539, 8540, 8541, 8544, 8545, 8546, 8547, 8548, 8552,  8553, 8554, 8555, 8558, 8559, 8560, 8561, 8562,  8565, 8566, 8567, 8568, 8569, 8573, 8574, 8575, 8576,  8579, 8580, 8581, 8582, 8583,  8586, 8587, 8588, 8589, 8590,8593, 8594, 8595,  8596, 8597, 8600, 8601,  8602, 8603, 8604, 8607, 8608, 8609, 8610, 8611, 8614, 8615, 8616,  8617, 8618,  8621, 8622, 8623,8624, 8625,8628, 8629, 8630, 8631, 8632, 8635, 8636, 8637,  8638, 8639, 8644, 8645, 8646, 8649, 8650, 8651, 8652, 8653, 8656, 8657, 8658, 8659, 8660, 8663,  8664, 8665, 8666, 8667, 8670, 8671, 8672, 8673, 8674,  8677, 8678, 8679, 8680, 8681, 8684, 8685, 8686, 8687, 8688, 8691, 8692, 8693, 8694,8695, 8698, 8699,  8700, 8701,8702, 8705, 8706, 8707, 8708, 8709, 8712, 8713, 8714, 8715, 8716, 8719, 8720, 8721, 8722, 8723, 8726, 8727, 8728, 8729, 8730, 8733,8734, 8735,  8736,  8737, 8740, 8741, 8742, 8743, 8744, 8747, 8748, 8749, 8750, 8751, 8754, 8755, 8756, 8757, 8758, 8761, 8762, 8763, 8764, 8765, 8768, 8769, 8770,  8771), class = "Date"), class = "zoo")

  df<-data.frame(ts)
  df<-data.frame(Date=as.Date(rownames(df)),Y=df$Close)
      df<-df[!is.na(df$Y),]
  library(minpack.lm)
  library(ggplot2)
  df$days<-as.numeric(df$Date-df[1,]$Date)
      f<-function(pars,xx){pars$a + (pars$tc - xx)^pars$m *(pars$b+ pars$c *        cos(pars$omega*log(pars$tc - xx) + pars$phi))}
      resids<-function(p,observed,xx){df$Y-f(p,xx)}

 nls.out <- nls.lm(par=list(a=6,b=-6,tc=3000, m=.4,omega=10,phi=-2,c=-1),fn = resids, observed = df$Y, xx = df$days, control= nls.lm.control (maxiter =1024, ftol=1e-6, maxfev=1e6))
 Warning messages:
1: In log(pars$tc - xx) : NaNs produced
    2: In log(pars$tc - xx) : NaNs produced
3: In log(pars$tc - xx) : NaNs produced
    4: In log(pars$tc - xx) : NaNs produced
5: In log(pars$tc - xx) : NaNs produced
nls.out
Nonlinear regression via the Levenberg-Marquardt algorithm
parameter estimates: 1292.85251942153, -14.1403675964815, 871.068726297531,   0.682341485852459, 0.742986030555774, 88.600462385114, 8.15118775146334 
residual sum-of-squares: 247649
reason terminated: Relative error in the sum of squares is at most `ftol'.

nls.out <- nls.lm(par=list(a=6,b=-6,tc=3000, m=.4,omega=10,phi=-2,c=-1),fn = resids, observed = df$Y, xx = df$days, control= nls.lm.control (maxiter =1024, ftol=1e-9, maxfev=1e6))
Warning messages:
1: In log(pars$tc - xx) : NaNs produced
    2: In log(pars$tc - xx) : NaNs produced
3: In log(pars$tc - xx) : NaNs produced
    4: In log(pars$tc - xx) : NaNs produced
5: In log(pars$tc - xx) : NaNs produced

nls.out <- nls.lm(par=list(a=6,b=-6,tc=3000, m=.5,omega=10,phi=-2,c=-1),fn = resids, observed = df$Y, xx = df$days, control= nls.lm.control (maxiter =1024, ftol=1e-9, ma xfev=1e6))
 Warning messages:
 1: In log(pars$tc - xx) : NaNs produced
     2: In log(pars$tc - xx) : NaNs produced
 3: In log(pars$tc - xx) : NaNs produced
     4: In log(pars$tc - xx) : NaNs produced
 5: In log(pars$tc - xx) : NaNs produced
     6: In log(pars$tc - xx) : NaNs produced

nls.out <- nls.lm(par=list(a=6,b=-6,tc=3000, m=.2,omega=10,phi=-2,c=-1),fn = resids, observed = df$Y, xx = df$days, control= nls.lm.control (maxiter =1024, ftol=1e-9, maxfev=1e6))
  Warning messages:
 1: In log(pars$tc - xx) : NaNs produced
     2: In log(pars$tc - xx) : NaNs produced
 3: In log(pars$tc - xx) : NaNs produced
     4: In log(pars$tc - xx) : NaNs produced
 5: In log(pars$tc - xx) : NaNs produced
     6: In log(pars$tc - xx) : NaNs produced
 7: In log(pars$tc - xx) : NaNs produced
     8: In log(pars$tc - xx) : NaNs produced
 9: In log(pars$tc - xx) : NaNs produced
     10: In log(pars$tc - xx) : NaNs produced
```

I tried many difference initial values but i couldn't set anything. Your help will be highly appreciated. You may refer the model in the following paper screen 33 (eq.2.9).